Problem: Rewrite as a simplified fraction. ${1.38\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1386.6666...\\ 100x &= 138.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1248}$ ${x = \dfrac{1248}{900}} $ ${x = \dfrac{104}{75}} \text{or} {1 \dfrac{29}{75}}$